面向飞行器概念设计的动网格技术

在弹簧近似光滑法和局部网格重构法两种动网格方法的基础上,结合类型函数/形状函数方法,针对飞行器概念设计阶段方案多变、参数变化快的特点,对二元机翼随参数变化的翼型提出了相适应的动网格方法.该方法根据参数的影响,将变动的边界信息传递到网格上,网格随之迭代变化.相对于常用动网格方法,该方法具有更强的参数表现力和适应力,使得网格生成更快速.对类型函数/形状函数转换方法(CST)拟合的NACA2415翼型在不同迎角情况下的低速湍流流动进行了数值模拟.计算结果表明,该动网格技术较好地模拟出了翼型的流动特性,较准确地得出了翼型的气动力系数,对飞行器概念设计阶段的参数确定具有实用价值,显示了该动网格方法的准确性和便捷性.     

一种改进的B 样条翼型参数化方法

翼型设计是空气动力学研究的一项重要内容,翼型的参数化结果将影响翼型的优化设计。为了减少翼型优化中的设计变量,保证优化结果的光滑性与C2 连续,在优化过程中控制翼型几何特性的变化范围,提出了一种改进的B 样条参数化方法。用一条三次非均匀B 样条曲线表示翼型,翼型数据的参数化过程中主要运用了B 样条曲线拟合算法,并且在一般的B 样条曲线拟合算法的基础上加入了对曲线的法向约束,通过迭代得到最终的参数化结果。实验结果表明,该方法可以很好的拟合典型的翼型数据,得到的翼型参数化结果不仅光滑,满足C2 条件,而且所得翼型函数的参数个数比传统的参数化方法有了进一步的减少,更有利于之后翼型的优化设计。     

基于二项式系数设计矩阵的Bézier曲线扩展

根据二项式的展开系数,设计出带形状参数的正系数矩阵,并对Bernstein基函数进 行具有明显几何意义的构造,推导出同阶带参的A-Bernstein基函数,该基函数具有Bernstein基函 数类似的性质。在此基础上推导出对应的A-Bézier曲线,分析了其不但具有Bézier曲线类似的性质, 而且在原始控制点不变的情况下,可以通过修改形状参数来对曲线进行调整。此外,还进一步说 明了可以通过对正系数矩阵的调整,实现对曲线的调整。通过举例,展现出该方法灵活有效。     

基于整数维约束的分维形状映射生成方法

把整数维图形研究方法与分数维图形研究方法相结合，提出一种基于整数维规则几何形状的约束的分维形状映射生成方法，有于描述自然界和工程中出现的且具有特定基本形状趋势的随机现象和随机过程，首先，任意选取一个具有调配函数的自由形状构造一个有序参数空间，确定有序参数的取值规律和区域，把有序参数空间与自适应神经网络，随机性相结合，构造一个随机离散参数空间，并建立起有序参数与随机离散参数之间的参数对应关系，最后，通过有序与无序的参数对应关系，建立一个独立于任意规则几何形状的统一的分形映射关系，对相应整数维的任意规则参数几何形状分形映射，生成宏观形态趋势可预见和可控制的分维形状，该提出的方法适有于任意参数几何形状的分形映射，生成分形图形，且方法简明，易于实现。     

连续体结构的参数化水平集统一优化

针对传统分步式结构优化设计的不足,提出一种同时进行结构拓扑、形状和尺寸统一优化的设计方法.首先采用水平集函数描述统一的结构优化模型和几何尺寸边界,通过引入紧支径向插值基函数将结构拓扑优化变量、形状优化变量和尺寸优化变量变换为基函数的扩展系数;然后取该扩展系数为设计变量,借助一种参数的变化表达3种优化要素对结构性能的影响,将复杂的多变量优化问题变换为相对简单的参数优化问题,有利于与相对成熟的优化算法相结合提高求解效率;进一步用R函数将其融合为一个整体,构造出统一优化模型,并用最优化准则法进行求解.最后通过数值案例证明了该方法的有效性和精确性.     

改变飞机变体机翼优化方法与气动特性仿真

为使变翼型便携式小型无人机拥有低起飞速度和较高的巡航速度,快速到达目的地的同时能有效改善无人机以不同方式起飞的性能,采用B样条方法描述翼型形状,用XFOIL软件进行气动计算,用遗传算法进行迭代计算,对无人机的翼型形状进行优化设计,得到了一个可以由巡航阶段翼型简单变化而来的改善飞机起飞性能的翼型形状.采用CFD仿真软件对翼型升阻力特性进行分析,并获得了采用变体技术的飞机在巡航阶段翼型和起飞阶段翼型的气动参数.最后通过对变体无人机和非变体无人机以不同方式起飞的起飞轨迹的仿真计算、比较证明了采用变翼型技术的无人机在采用不同方式起飞时都能有效改善起飞性能.     

带双形状参数的C-B样条曲线

利用积分方法构造了带双形状参数的C-B样条曲线基函数,这类曲线具有标准C-B样条曲线主要性质,如连续性、凸包性等;根据形状参数的不同取值可以整体或者局部调控曲线形状,由此生成的曲线与曲面,作为一种新的几何造型方法,可应用于CAD/CAM领域。     

双三次Coons曲面片的两种扩展*

为解决传统双三次Coons曲面片在给定边界条件时其形状难以调整的不足,给出了一组带形状参数的Hermite基函数,并基于该基函数构造了一种带两个形状参数的Coons曲面片,称之为QC-Coons曲面片;然后通过对基函数重新参数化,构造了一种带两个形状参数的有理Coons曲面片,称之为RQC-Coons曲面片。结果表明,所构造的两种新曲面片都是双三次Coons曲面片的扩展,它们不仅具有双三次Coons曲面片的性质,而且还可通过调整形状参数的取值使得曲面的内部表现出不同的形状,为Coons曲面片的设计提供了两     

T-Bézier曲线及G1拼接条件

针对目前NURBS模型的局限性问题,在对T-Bézier基函数及曲线端点特性分析的基础上,提出了k次T-Bézier基函数的表达式,通过重新参数化使其参数区间范围规范为[0,1],给出了椭圆弧和心脏线的T-Bézier表示,并给出T-Bézier曲线间G1拼接的几何条件,所得结论具有明确的几何意义,能够较好地应用于曲面造型中。     

带多形状参数的广义Bézier曲线曲面

为了在几何造型中更加灵活地调控曲线曲面的形状,提出一种带多形状参数的造型方法.首先构造一种带多形状参数的多项式调配函数,其中Bernstein基函数是它的特例;然后利用给出的调配函数定义一类形状可调的广义Bézier曲线曲面,并研究了它们的性质.对给定的控制多边形,可以通过改变形状参数的值整体或局部地调控曲线的形状.最后通过数值实例说明了文中方法的实用性.     

Equivalence of continuum and discrete analytic sensitivity methods for nonlinear differential equations

This paper presents results for the study of equivalence between the total form continuum sensitivity equation (CSE) method and the discrete analytic method of shape design sensitivity analysis. For the discrete analytic method, the sensitivity equations are obtained by taking analytic derivatives of the discretized equilibrium equations with respect to the shape design parameters. For the CSE method, the equilibrium equations are firstly differentiated to form a set of linear continuous sensitivity equations and then discretized for solving the shape sensitivities. The sensitivity equations can be derived by taking the material derivatives (total form) or the partial derivatives (local form) of the equilibrium equations. The total form CSE method is shown for the first time to be equivalent, after finite element discretization, to the discrete analytic method for nonlinear second-order differential equations of a particular form with design dependent loads when they use the same: (1) finite element discretization, (2) numerical integration of element matrices, (3) design velocity fields that are linear with respect to the design variable and (4) shape functions for domain transformation and for design velocity field calculations. The shape sensitivity equations for three-dimensional geometric nonlinear elastic structures and linear potential flow are derived by using both total form CSE and discrete analytic method to show the equivalence of the two methods for these specific examples. The accuracy of shape sensitivity analysis is verified by potential flow around an airfoil and a joined beam with an airfoil under gust load. The results show that analytic sensitivity results are consistent with the complex step results.     

基于几何活动轮廓模型的人脸轮廓提取方法

针对在结构性噪声较严重的情况下 ,常规几何活动轮廓模型无法获得理想分割效果的问题 ,提出一种基于几何活动轮廓模型的人脸轮廓提取方法 ,该方法首先将人脸形状的椭圆性约束作为算子嵌入到几何活动轮廓模型中 ,并利用几何活动轮廓模型提取任意轮廓的优势来快速抽取出图象中类似椭圆的目标边缘 ;然后根据图象中人脸的先验知识 ,通过对检测到的椭圆目标进行进一步验证来找出最终人脸轮廓 .由于采用变分水平集方法做数值计算 ,因此该方法不仅能够自然地处理曲线的拓扑变化和能较精确地提取出图象中的人脸轮廓 ,而且同时可以给出人脸水平旋转的大致角度等信息 .实验结果表明 ,该方法是有效的 .     

双重轮廓演化曲线的图像分割水平集模型

目的几何活动轮廓模型的标志性模型C-V模型及其改进LBF模型受到关注,然而这两个模型对初始轮廓曲线较强的依赖性使得模型在实际图像目标分割中表现出不稳定性或具有较高的时间复杂性。本文在对C-V模型及LBF模型的原理及对初始轮廓曲线的依赖特性进行分析的基础上,提出一种基于双重轮廓演化曲线的图像分割水平集模型。方法所提出模型的主要过程如下:1)通过设置内、外两条轮廓线,使模型在演化过程中分别从目标的内部和外部向目标边界逼近,两条轮廓线的设计原则简单,其分别位于目标的外部和与目标有重叠;2)两条轮廓线的演化走向是通过在模型中设置相关项自动控制的,即演化过程中通过最小化内、外轮廓之间的差异来自动控制两条轮廓曲线的演化趋向,使之同时从目标的内部和外部向目标边界逼近,并逐渐稳定于目标的边界。结果所提出的模型通过设置内部能量泛函项,避免了对符号距离函数的重新初始化;通过采用全局化的正则函数,增加了模型对复杂异质区域边界的捕捉能力;通过采用内、外轮廓线同时演化机制,避免了模型对初始轮廓线的过依赖性。结论所提出的模型很好地解决了传统基于区域的分割模型对轮廓曲线初始化的过依赖问题,对初始轮廓线的设置较为简单且具有较强的鲁棒性,对图像目标的分割较为准确和稳定。     

拱序列的曲线描述与匹配

目的 曲线匹配是计算机视觉和图像处理中的一个重要问题;判定几何图形形状相似性,得到与人类认知一致的结果,是目前的曲线描述与分类算法不能很好解决的问题。针对曲线匹配和几何图形形状的相似性判定,提出一种有效快速的基于拱序列的曲线匹配与相似性判定算法。方法 提取曲线的角点,将曲线表示为一连串相互重叠的拱序列。对于拱序列中的每一个拱,使用拱描述子进行描述。利用拱描述子,使用动态规划方法,实现对拱序列的匹配和相似性判定。结果 为了验证本文算法,将基于拱序列的曲线描述与匹配方法应用于轮廓的拼接与几何图形的相似性比较。在轮廓拼接实验中,基于拱序列的曲线描述与匹配方法准确完成碎片轮廓的拼接和地图轮廓的拼接。在几何图形相似性的交叉度量实验中,基于拱序列的曲线描述与匹配方法可以准确反映出图形的相似程度,正确判断两幅图像是否属于同一类型。在判定不同相似程度的形状对的实验中,本文算法可以给出与人类判断相同的结果,相比较基于链码特征、多尺度不变量、形状上下文和GCT（geometry complex transform）变换算法,本文算法的距离值更好地反映出图像的相似程度。结论 理论和实验表明,该算法可有效地描述曲线、匹配曲线,及准确判断几何图形的相似性,给出与人类视觉判定一致的结果。该算法可用于基于轮廓的图像拼接和几何图形相似性的判定。     

Hybrid path planning method based on skeleton contour partitioning for robotic additive manufacturing

Establishing manufacturability design criteria for multidimensional complex parts can significantly reduce the production cost, shorten the manufacturing cycle, and improve the production quality of directed energy deposition. Therefore, there is an urgent need to establish a high-performance manufacturing design strategy for complex parts. Proposed here is a skeleton contour partitioning hybrid path-planning method that takes full advantage of the excellent geometric reducibility of the contour offset method and the outstanding flexibility of the zigzag path method, eliminating the influences of sharp corners and degradation on forming quality in the contour offset method. First, reference contours are obtained by subjecting the original contours to an inward–outward twice-offset process; incompletely filled regions are obtained by Boolean operations on the original and reference contours, and these regions are the ones to be optimized. Second, the optimized regions are merged into skeleton fill regions, and the fill paths are generated by a polygon trapezoidal partitioning recombination algorithm and an algorithm for generating optimal zigzag paths. Finally, the contour offset paths are split and regrouped based on the skeleton regions and are connected into a continuous forming path for each subregion, then all the forming paths are converted into robot printing tool paths from the skeleton-region filling paths to the contour-offset ones. The actual forming results for several parts with different geometric features are verified and compared with those of the traditional path-planning method, and it is concluded that the proposed method converges rapidly to the details of complex components and is highly feasible and applicable.     

一种基于多尺度轮廓点空间关系特征的形状匹配方法

针对使用三角形区域表示描述子对相似形状进行匹配时,对微小形变比较敏感 以及区分剧烈变化的不相似形状时判别能力较弱的问题, 提出一种结合轮廓点空间关系特征的多尺度形状特征描述子.通过分析不同尺度下参考点与其他采样点之间的位置关系, 利用对应角度信息来对形状进行表示, 并在此基础上构造出一种新的形状特征描述子.本文所提特征提取方法能对形状的局部及全局信息更准确地描述, 具有较好的鲁棒性和判别能力.在形状特征匹配阶段, 利用轮廓点集顺序关系已知这一优势, 引入动态规划及形状复杂度分析的方法,分析形状间的匹配结果, 能够得到较好的形状匹配精度.通过对不同形状数据集行仿真实验, 证明本文方法能够有效地实现形状识别和检索.     

Adaptive locally affine-invariant shape matching

Matching deformable objects using their shapes are an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class variations, local deformations, articulations, viewpoint changes and missed and extraneous contour portions due to errors in shape extraction. While small local deformations have been handled in the literature by allowing some leeway in the matching of individual contour points via methods such as Chamfer distance and Hausdorff distance, handling more severe deformations and articulations has been done by applying local geometric corrections such as similarity or affine. However, determining which portions of the shape should be used for the geometric corrections is very hard, although some methods have been tried. In this paper, we address this problem by an efficient search for the group of contour segments to be clustered together for a geometric correction using dynamic programming by essentially searching for the segmentations of two shapes that lead to the best matching between them. At the same time, we allow portions of the contours to remain unmatched to handle missing and extraneous contour portions. Experiments indicate that our method outperforms other algorithms, especially when the shapes to be matched are more complex.     

Higher Order Active Contours

We introduce a new class of active contour models that hold great promise for region and shape modelling, and we apply a special case of these models to the extraction of road networks from satellite and aerial imagery. The new models are arbitrary polynomial functionals on the space of boundaries, and thus greatly generalize the linear functionals used in classical contour energies. While classical energies are expressed as single integrals over the contour, the new energies incorporate multiple integrals, and thus describe long-range interactions between different sets of contour points. As prior terms, they describe families of contours that share complex geometric properties, without making reference to any particular shape, and they require no pose estimation. As likelihood terms, they can describe multi-point interactions between the contour and the data. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Networks are a shape family of great importance in a number of applications, including remote sensing imagery. To model them, we make a particular choice of prior quadratic energy that describes reticulated structures, and augment it with a likelihood term that couples the data at pairs of contour points to their joint geometry. Promising experimental results are shown on real images.     

Geometric algorithm for dominant point extraction from shape contour

In this paper we propose a new algorithm for extracting dominant points from the real contour of a digital shape. A polygonal approximation of the shape can be obtained by the set of dominant points. In the proposed algorithm, in the first step before searching for dominant points, the real contour is made sparse using a geometric concept, named convex deficiency tree. This helps to select a set of candidate points from real contour. In comparison with break points (which are initial points in many algorithms), the set of candidate points is more heuristic and the ratio of them to the all points of the contour is lower. In the second step of the proposed algorithm, the less informative candidate points are removed in an iterative manner. After removing one candidate point, its adjacent positions are searched to find more stable position for its neighbors. The comparative result of the proposed algorithm with others shows its efficiency. The algorithm finds an effective polygonal approximation for digital shapes especially for the real contours, which makes the method more practical.